Extension of Chekanov-Eliashberg algebra using annuli
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910596090298368 |
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| author | Dukic, Milica |
| author_facet | Dukic, Milica |
| contents | We define an SFT-type invariant for Legendrian knots in the standard contact $\mathbb{R}^3$. The invariant is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential consists of a part that counts index zero $J$-holomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological part. We describe the invariant and demonstrate its invariance combinatorially from the Lagrangian knot projection, and compute some simple examples where the deformation is non-vanishing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extension of Chekanov-Eliashberg algebra using annuli Dukic, Milica Symplectic Geometry 53D42, 57K33, 57R17, 53D12 We define an SFT-type invariant for Legendrian knots in the standard contact $\mathbb{R}^3$. The invariant is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential consists of a part that counts index zero $J$-holomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological part. We describe the invariant and demonstrate its invariance combinatorially from the Lagrangian knot projection, and compute some simple examples where the deformation is non-vanishing. |
| title | Extension of Chekanov-Eliashberg algebra using annuli |
| topic | Symplectic Geometry 53D42, 57K33, 57R17, 53D12 |
| url | https://arxiv.org/abs/2409.05856 |